The Convolution Method
Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) lesson in Severity, Frequency, and Aggregate Models. 7 min read, ~1,094 words.
Discrete convolution:. For more variables: convolve iteratively, first, then add. Collective risk model: condition on, then compute n-fold convolution for each. Exam strategy: only enumerate pairs that produce the target sum, not the full distribution. Verification: probabilities must sum to 1.
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